Folks,

I need to show that $\displaystyle \int_\Omega (\nabla G)w dxdy=-\int_\Omega (\nabla w) G dxdy+\int_\Gamma \hat{n} w G ds$ given

$\displaystyle \int_\Omega \nabla F dxdy=\oint_\Gamma \hat{n} F ds$ where $\displaystyle \Omega$ and$\displaystyle \Gamma$ are the domain and boundary respectively. F,G and w are scalar functions...any ideas?

I attempted to expand the LHS but I didnt feel it was leading me anywhere...

$\displaystyle \displaystyle \int_\Omega (\hat{e_x}\frac{\partial G}{\partial x}+\hat{e_y}\frac{\partial G}{\partial y})w dx dy$....?